Two circles touch externally at a point P. From a point T on the tangent at P,

Question:

Two circles touch externally at a point P. From a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively. Prove that TQ = TR.

Solution:

We know that the lengths of tangents drawn from an external point to a circle are equal.

In the given figure, TQ and TP are tangents drawn to the same circle from an external point T.

∴ TQ = TP               .....(1)

Also, TP and TR are tangents drawn to the same circle from an external point T.

∴ TP = TR               .....(2)

From (1) and (2), we get

TQ = TR

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